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gptkbp:instanceOf
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gptkb:Weyl_group
gptkb:group_of_people
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|
gptkbp:automorphismGroup
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contains field, graph, and diagonal automorphisms
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gptkbp:centralTo
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cyclic group of order gcd(2, q-1)
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|
gptkbp:definedIn
|
finite field of order q
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|
gptkbp:Dynkin_diagram
|
E7
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|
gptkbp:hasMaximalTorus
|
yes
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|
gptkbp:hasParabolicSubgroups
|
yes
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|
gptkbp:isAdjointForm
|
when center is trivial
|
|
gptkbp:isGroupOfLieType
|
true
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|
gptkbp:isPartOfClassification
|
finite simple groups
|
|
gptkbp:isPerfect
|
true
|
|
gptkbp:isQuasisimple
|
true
|
|
gptkbp:isSimple
|
q > 2
true for q > 2
|
|
gptkbp:isSplitForm
|
true
|
|
gptkbp:isUniversalForm
|
when center is maximal
|
|
gptkbp:order
|
q^{63}(q^{2}-1)(q^{6}-1)(q^{8}-1)(q^{10}-1)(q^{12}-1)(q^{14}-1)(q^{18}-1)/gcd(2,q-1)
|
|
gptkbp:rank
|
7
|
|
gptkbp:relatedTo
|
gptkb:E7_Lie_algebra
gptkb:exceptional_groups_of_Lie_type
gptkb:E7_Weyl_group
gptkb:algebraic_group_E7
|
|
gptkbp:bfsParent
|
gptkb:exceptional_groups_of_Lie_type
gptkb:finite_Chevalley_group
gptkb:groups_of_Lie_type
gptkb:finite_group_of_Lie_type
|
|
gptkbp:bfsLayer
|
9
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
E7(q)
|